Snow flakes are one of nature’s beauties which are easy to appreciate even for the more mathematically or technically minded. Kenneth G. Libbrecht produces wonderful photographs of them; some are available online.
The symmetry of snow flakes is described by the dihedral group. This is one of the first groups described in Felix Klein’s book I have advertised before. Here is my illustration of how Klein described this group geometrically.
Glimpses of a fascinating world 